Pour the bourbon in a cup ¾ full of shaved ice. Bruise 2 or 3 mint sprigs with your fingers and rub over the rim of the cup. Dissolve the sugar in the water in a small bowl. Stir the sugar solution gently into the bourbon. Add enough additional shaved ice to fill the cup. Garnish with an additional mint sprig.

Muddle mint with ¼ ounce simple syrup in a cocktail shaker. Pour in the rest of the liquids and add ice to fill shaker 3/4 full. Stir with a cocktail spoon until chilled and diluted slightly. Strain into a chilled coupe glass and garnish with sprig of mint.